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SSC CHSL Population Problems

Study Material — 1 PYQs (2018–2018) · Concept Notes · Shortcuts

SSC CHSL Population Problems is a frequently tested subtopic — 1 previous year questions from 2018–2018 papers are included below with concept notes, key rules and shortcut tricks.

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2018–2018
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Previous Year Questions

SSC CHSL Population Problems — Past Exam Questions

1 questions from actual SSC CHSL papers · all shown free · click option to reveal solution

Exam Q 12018Previous Year Pattern

The population of a city was 8,00,000 in 2020. It increased by 15% in 2021 and decreased by 10% in 2022. In 2023, it again increased by 20%. What is the population of the city at the end of 2023?

Concept Notes

Population Problems— Rules & Concept

Core ConceptRead this first — the foundation of the topic
CORE CONCEPT

Population problems follow the compound growth formula. If a population increases or decreases by a certain percentage each year, you apply that percentage repeatedly, not just once. This is different from simple interest — it's like compound interest

KEY RULES

Population grows or shrinks by a fixed percentage each year 2. The percentage applies to the NEW population each year, not the original 3. Use the compound formula, not simple addition/subtraction 4. Decrease and increase work the same way mathematically

Formula BlockMemorise — at least one formula appears in every paper
Final Population = Initial Population × (1 + r/100)^n

Where:

- r = rate of increase (use negative r for decrease)
- n = number of years
- If r = 5% increase, use (1 + 5/100) = 1.05
- If r = 10% decrease, use (1 - 10/100) = 0.90
Exam PatternsWhat examiners ask — read before attempting PYQs
1

Find final population after n years

2

Find initial population (work backwards)

3

Find rate of growth

4

Find time period

5

Mixed increase and decrease over different years

Worked ExampleSolve this step-by-step before moving on
1
Step 1

Population after Year 1 = 50,000 × (1 + 10/100) = 50,000 × 1.10 = 55,000

2
Step 2

Population after Year 2 = 55,000 × (1 + 20/100) = 55,000 × 1.20 = 66,000 Alternative Direct Method: = 50,000 × 1.10 × 1.20 = 50,000 × 1.32 = 66,000

Exam TrapsCommon mistakes students make — avoid these

Students add percentages directly: 10% + 20% = 30%, then calculate 50,000 × 1.30 = 65,000. This is WRONG because the 20% applies to the increased population, not the original. Always multiply the factors for each year.

Key Points to Remember

  • Population problems use compound growth formula: Final = Initial × (1 + r/100)^n
  • Percentage always applies to the CURRENT population, not the original amount
  • For decrease, use (1 - r/100) in the formula instead of (1 + r/100)
  • Multiple years with different rates: multiply all factors together for direct calculation
  • Never add percentages directly; always use multiplication of decimal factors
  • If asked for initial population, rearrange formula: Initial = Final ÷ (1 + r/100)^n

Exam-Specific Tips

  • Population formula: Final = Initial × (1 + r/100)^n where r is annual rate and n is years
  • For 10% increase, multiply by 1.10; for 10% decrease, multiply by 0.90
  • If population increases by p% one year and q% next year, combined factor = (1 + p/100) × (1 + q/100)
  • Compound population growth applies the percentage to the NEW amount each year, not original
  • For population decrease problems, the formula remains the same but r is treated as negative
  • Quick check: 50,000 population growing at 10% annually for 2 years = 50,000 × 1.21 = 60,500
Practice MCQs

Population Problems — Practice Questions

22graded MCQs · easy to hard · full solution & trap analysis · showing 20 of 22

All MCQs →
Practice 1easy

The population of a city was 500,000 in 2020. If it increased by 20% in 2021, what was the population at the end of 2021?

Practice 2easy

A town's population decreased by 15% over one year. If the population at the end of the year was 170,000, what was the population at the beginning of the year?

Practice 3easy

In 2019, a village had 80,000 people. In 2020, the population increased by 25%. In 2021, it increased by 10%. What was the population in 2021?

Practice 4easy

If a region's population increases from 400,000 to 480,000, what is the percentage increase?

Practice 5easy

The population of village A is 80,000 and the population of village B is 120,000. By what percentage is village B's population more than village A's population?

Practice 6easy

A city's population was 250,000 in 2018. By 2020, it had grown to 360,000. What was the percentage increase in population over these two years?

Practice 7easy

A district's population was 600,000. After a 30% increase, what is the new population?

Practice 8medium

In a city, the population increased from 4,00,000 to 4,84,000 over two years. If the increase in the first year was 10%, what was the percentage increase in the second year?

Practice 9medium

A town's population increases by 25% every year. If the population was 1,28,000 at the end of 2021, what was the population at the end of 2019?

Practice 10medium

The population of a city increases by 20% in the first year and then decreases by 10% in the second year. If the population after 2 years is 216,000, what was the initial population?

Practice 11medium

A town's population was 500,000 in 2015. It increased by 15% by 2018 and then decreased by 20% by 2021. What is the population in 2021?

Practice 12medium

In a city, the male population is 55% of the total. If the female population is 180,000, what is the total population of the city?

Practice 13medium

A city's population was 250,000 in 2010. By 2015, it became 300,000. By 2020, it became 360,000. What is the percentage increase from 2015 to 2020 compared to the increase from 2010 to 2015?

Practice 14medium

The population of a city was 5,00,000 in 2020. It increased by 20% in 2021 and then decreased by 10% in 2022. What is the population at the end of 2022?

Practice 15medium

The male population of a village is 60% of the total population. If the female population is 8,000, what is the total population of the village?

Practice 16hard

In a city, 35% of the population are children and 60% are adults. The remaining population consists of senior citizens. If there are 1,50,000 senior citizens, what is the total population of the city?

Practice 17hard

A state's population increased from 80 lakhs to 1 crore in 5 years. What is the average annual percentage increase in population?

Practice 18hard

In a district, the population of males increased by 15% and the population of females increased by 20% over a decade. If the male population increased by 3,60,000 and female population increased by 4,80,000, what was the total population of the district a decade ago?

Practice 19hard

A region's population was 8,00,000 five years ago. It increased by 10% in the first two years combined, then by 20% in the next two years, and by 5% in the fifth year. What is the current population?

Practice 20hard

The population of a city was 5,00,000 in 2015. It increased by 20% in the next 4 years and then decreased by 10% in the following 2 years. What is the population in 2021?

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60-Second Revision — Population Problems

  • Formula: Final Population = Initial × (1 + r/100)^n — this is compound, not simple
  • Trap: Never add percentages from different years. Multiply the growth factors instead
  • Decrease: Use negative r or write (1 - r/100) — both methods give same answer
  • Multi-year: For different rates each year, write as Initial × (1.10) × (1.20) × (0.95) etc.
  • Reverse: If given final population, divide backwards: Initial = Final ÷ [(1 + r/100)^n]
  • Quick mental check: 10% increase twice ≈ 21% total (not 20%), because second 10% acts on larger base
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